TTI‘s resident columnist Joe Walter considers the application of symmetry and asymmetry in tire design.
Symmetry in various forms occurs in nature and in man-made products. It permeates disciplines ranging from the visual arts and music to biology and the physical sciences. Tires themselves are rotationally symmetric bodies of revolution. Birds, butterflies and human beings possess so-called bilateral symmetry dividing their shapes into left and right halves that are mirror images of one another – although internal organs are usually arranged asymmetrically. Bilateral symmetry is easily recognized and is thought to have evolved in animals because it conferred advantageous movement – known as ‘directed locomotion’ with the potential for streamlining. Most automobiles, airplanes and ships are also outwardly symmetric about their vehicle pitch plane.
Tire tread patterns can exhibit various types of symmetry depending on the product line. The most important class, known as combined point and rotational symmetry, is used on the vast majority of car, truck and SUV tires. Importantly, tires with tread patterns featuring this two-fold symmetry can be mounted in multiple ways on a vehicle (left or right; front or rear) – a convenience preferred by most consumers. Geometrically, if the tire tread pattern remains invariant after a 180° rotation about a fixed point, the pattern is both point and rotationally symmetric. Some everyday non-automotive objects also possess this dual symmetry, including the face cards in a deck of cards. In other words, like most tread patterns, these cards remain the same when turned upside down.
The two-dimensional footprint of a directional tire exhibits so-called line or mirror symmetry – the planar analog of bilateral symmetry. Directional tread patterns, often used on high-performance tires, feature V-shaped ribs and grooves symmetrically disposed shoulder-to-shoulder about the centerline of the tread. Such imagery is characteristic of line symmetry; it infers that each half of a 2D pattern is a reflection of the other. Directional tires with their striking tread patterns are designed to roll one way only, and because of this limitation remain niche products in the automotive market. The medial line of a tire cross-section also exhibits mirror symmetry.
Asymmetric tire tread patterns possess no point, rotational or mirror symmetry and have a limited, but growing, market-driven appeal. The outboard portion of such treads is generally ‘blockier’ to enhance dry cornering, while the inboard region features smaller blocks with grooves and sipes that promote wet traction. Such tires are nominally side-bound – that is, designed to operate on either the left- or right-hand side of a vehicle. The Michelin XAS was the first tire (1965) to purposefully feature tread pattern asymmetry and the first production tire to operate at 130mph (210km/h). Interestingly, the locomotion pattern of the human foot served as the inspiration for the design of the XAS.
In contrast, certain asymmetries known as conicity and ply steer, among others, unavoidably occur in radial tire lateral force behavior. These inherent offsets arise due to manufacturing imprecision and the stacking sequence and orientations of the plies, respectively. These side forces perpendicular to the wheel plane are negligibly small in bias ply tires and usually dismissed as non-issues. In radial constructions, these steering-like forces exist even at zero slip and camber angles. Ply steer, or pseudo-slip, mainly results in vehicle ‘dog tracking’ while conicity, or pseudocamber, produces torque at the steering wheel – known as ‘pull’. Fortunately, ply steer is a deterministic variable that can be determined at the design stage of tire development, while conicity is a random factory variable that is measured post-production using a tire uniformity machine.
Asymmetry can be purposefully exploited in some tire constructions for improved tire-vehicle behavior. For example, steel belts have been intentionally positioned slightly off-center during tire assembly to induce a consistently positive or negative bias in conicity values; similar results can be achieved by making tread depths slightly deeper on one shoulder than the other. These unsymmetrical features allow for balanced positioning of such tires on vehicle front axles during auto assembly operations, which mitigate steering wheel pull while driving. Furthermore, the patent literature dealing with asymmetrical tire constructions is replete with concepts never commercialized.
After spending portions of my career trying to understand, eliminate or control such nuanced tire design concepts involving symmetry and asymmetry, many of my past efforts could prove irrelevant in a future world of autonomous vehicles lacking discerning drivers.
